JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Three Dimensional Geometry

A general point of $L$ is $(3+2t,1+t,2+t)$, and the vector joining $(2,3,-1)$ to it is $(1+2t,t-2,3+t)$. This is perpendicular to the direction $(2,1,1)$ when

so the foot of the perpendicular is $F=\left(2,\frac{1}{2},\frac{3}{2}\right)$ and the image is

Since $L$ is perpendicular to $P$, the direction $(2,1,1)$ of $L$ is a normal to $P$, and the plane through $Q$ is

The point $(1,2,2)$ gives $2+2+2=6$, so $(1,2,2)$ lies on $P$.